faktorisieren 16x^4+4x^2y^2+y^4

Lösung

faktorisieren

16 x^{4} + 4 x^{2} y^{2} + y^{4}

(4 x^{2} + y^{2} + 2 x y) (4 x^{2} + y^{2} - 2 x y)

Schritte zur Lösung

16 x^{4} + 4 x^{2} y^{2} + y^{4}

Addiere und subtrahiere

4 x^{2} y^{2}

= 16 x^{4} + 8 x^{2} y^{2} + y^{4} - 4 x^{2} y^{2}

Faktorisiere

16 x^{4} + 8 x^{2} y^{2} + y^{4} : (4 x^{2} + y^{2})^{2}

= (4 x^{2} + y^{2})^{2} - 4 x^{2} y^{2}

Wende Exponentenregel an

= (4 x^{2} + y^{2})^{2} - (2 x y)^{2}

Faktorisiere

(4 x^{2} + y^{2})^{2} - (2 x y)^{2} : (4 x^{2} + y^{2} + 2 x y) (4 x^{2} + y^{2} - 2 x y)

= (4 x^{2} + y^{2} + 2 x y) (4 x^{2} + y^{2} - 2 x y)

s im pl i f y \frac{85 \cdot x ^{4}}{( x ^{3} ) ^{4}}

s im pl i f y \frac{( 20 x ^{10} )}{( 5 x ^{8} )}

e x p an d (5 x^{2} - 3 x)^{4}

s im pl i f y l^{- 1} \cdot {lo g_{10} (\frac{( s ^{2} - a ^{2} )}{( s ^{2} )})}

s im pl i f y 2 lo g_{10} (n^{n})